Quantum Latent Gauge and Coherence Selective Forces

TL;DR

The work proposes a coherence-selective hidden U(1) gauge field that couples to a conserved coherence current $\hat{J}^\mu_{\mathrm{(coh)}}$, defined via an operator-level coarse-graining of the Noether mass current, so that classical mixtures do not source the latent field while spatial superpositions and entangled states do. This yields three testable signatures: visibility-dependent interferometric phase shifts, $m^2$-scaled and non-Gaussian decoherence kernels, and entanglement-selective forces between distant massive qubits. The framework maintains gauge invariance, causality, and complete positivity in the appropriate limit, and it provides a complementary path to fifth-force searches by focusing on quantum coherence rather than classical densities. Near-term platforms including atom interferometers, levitated nanoparticles, and entanglement experiments can place first bounds on the coupling, offering a novel route to probe the quantum-classical boundary and potential coherence-based extensions of gravity and gauge interactions.

Abstract

We propose a hidden U(1) gauge interaction that couples exclusively to quantum coherence in massive systems. The central innovation is a conserved coherence current operator constructed from the Noether mass current via operator-level coarse-graining. This current vanishes for classical matter distributions but is nonzero for spatial superpositions and entangled states, yielding a gauge interaction that is dormant in classical regimes but activated by quantum coherence. The framework predicts three distinctive signatures: (i) interferometric phase shifts scaling linearly with fringe visibility, (ii) decoherence rates with characteristic m^2 scaling and spatial dependence distinct from collapse models, and (iii) entanglement-selective forces between distant massive qubits. The theory maintains full gauge invariance, causality, and positive time evolution. We show that state-of-the-art atom interferometers and levitated nanoparticles can place first constraints on this interaction class, complementary to classical fifth-force searches. This approach provides a novel theoretical framework for probing coherence-selective fundamental interactions and their potential role in the quantum-classical transition. To make this more concrete, we also spell out a simple benchmark latent-field model and work out, in detail, how a representative large-momentum-transfer atom interferometer constrains the corresponding coupling strength.

Figures (6)

• Figure 1: Conceptual illustration of the Quantum Latent Gauge (QLG) interaction. Right panel shows a single, smooth mass distribution that is effectively classical: it sources only the coarse-grained (classical) mass current and leaves the latent gauge field $A_\mu$ in a uniform, dormant configuration, indicated by straight field lines. Left panel shows a spatially coherent superposition with two separated lobes and interference structure: the off-diagonal elements of the density matrix generate a non-zero coherence current, which "activates" the QLG field and leads to a distorted, wavy field pattern. Classical mixtures with the same coarse-grained mass profile as in panel (b) would not excite the latent field, underscoring the coherence-selective nature of the coupling.
• Figure 2: QLG-induced phase shift $\Delta\phi_{\mathrm{QLG}}$ versus fringe visibility $\mathcal{V}$ for two representative values of the coupling $g$. The straight lines highlight the linear visibility dependence predicted by Eq. \ref{['eq:Delta_phi_scaling']}, with larger $g$ giving a steeper slope.
• Figure 3: Schematic comparison of spatial decoherence kernels as a function of separation $\Delta x$. The solid curve illustrates a representative QLG kernel with a non-Gaussian, oscillatory profile that saturates to a constant value for large $\Delta x$, as motivated by the benchmark form in Eq. (\ref{['eq:f_benchmark']}). The dashed curve shows a Gaussian kernel of fixed width, as used for example in CSL-type phenomenological models. The purpose of this figure is to highlight the qualitatively different large-distance behaviour and nonlocal structure of QLG-induced decoherence.
• Figure 4: (a) Decoherence rate $\Gamma$ versus superposition size $\Delta x$ for a fixed mass, comparing the Quantum Latent Gauge-induced decoherence channel (solid line) to a constant environmental contribution (dashed line). The latent-gauge contribution grows with $\Delta x$ and saturates once the branches are well separated. (b) Decoherence rate as a function of mass $m$ at fixed $\Delta x$ in log--log scale, highlighting the $m^2$ scaling of the Quantum Latent Gauge channel (solid line) relative to a mass-independent environmental rate (dashed line). For sufficiently large masses the Quantum Latent Gauge-induced decoherence becomes the dominant contribution.
• Figure 5: Illustrative QLG-induced signal as a function of the entanglement measure $C$ (concurrence) for three classes of two-qubit states: a pure entangled state (solid line), a partially mixed entangled state (dashed line), and a classical mixture with identical local statistics (dotted line). Only genuinely entangled states generate a nonzero signal, reflecting the entanglement-selective nature of the effective interaction in Eq. \ref{['eq:Heff_two_qubits']}.